Background: The feasibility of a user-specific finite element model for predicting the in

Transcription

1 1 Abstract Background: The feasibility of a user-specific finite element model for predicting the in situ strength of the radius after implantation of bone plates for open fracture reduction was established. The effect of metal artifact in CT imaging was characterized. The results were verified against biomechanical test data. Methods: Fourteen cadaveric radii were divided into two groups: 1) intact radii for evaluating the accuracy of radial diaphysis strength predictions with finite element analysis and 2) radii with a locking plate affixed for evaluating metal artifact. All bones were imaged with CT. In the plated group, radii were first imaged with the plates affixed (for simulating digital plate removal). They were then subsequently imaged with the locking plates and screws removed (actual plate removal). Fracture strength of the radius diaphysis under axial compression was predicted with three-dimensional, specimen-specific, nonlinear finite element analysis for both the intact and plated bone (bone with and without the plate captured in the scan). Specimens were then loaded to failure using a universal testing machine to verify actual fracture load. Findings: In the intact group, the physical and predicted fracture loads were strongly correlated. For radii with plates affixed, the physical and predicted (simulated plate removal and actual plate removal) fracture loads were strongly correlated. Interpretation: This study demonstrates that our specimen-specific finite element analysis can accurately predict the strength of the radial diaphysis. The metal artifact from CT imaging was shown to produce an over-estimate of strength

2 Introduction Open reduction internal fixation using plates is a commonly accepted treatment of diaphysis forearm fractures in adults (Hertel R et al., 2011). Previous reports describe excellent outcomes resulting from diaphysis fracture reduction with plates, but some complications such as nonunion and refracture after plate removal occurred (Leung F et al., 2006; Henle P et al., 2011). Clinical, quantitative techniques to assess healing are limited. Fluoroscopic and CT imaging are primarily used by physicians to assess callus formation quality or to determine if bone union has occurred. While useful, these tools falls short of characterizing bone strength at the healing site after bone union. In situ measurements of bone strength, would allow physicians to evaluate the degree of bone healing and the risk of refracture, and to decide on courses of treatment, for example the plate could be removed or not by knowing bone strength under the plate. Kettunen et al. measured the bone mineral density of the forearm bone shaft lying beneath a plate and reported that there was a small, partially reversible deficit (Kettunen J et al., 2003). However, mineral density is just one element of bone strength. Bone strength is defined by bone mineral density and bone quality (Klibanski A et al., 2001). Characteristics of bone quality include trabecular bone structure, geometry, microarchitecture, mineralization, crystallinity, collagen characteristics, microfracture, and bone turnover (Katsamanis F et al.1990; Davison KS et al, 2006). To our knowledge, there have been no studies reporting on the in situ human bone strength beneath plates during fixation Subject-specific finite element modeling (FEMs) is an effective tool for fracture strength assessment (Matsumoto T et a., 2009). Because FEMs can take into account bone geometry, architecture, and heterogeneous mechanical properties of bone, models based on QCT data may predict the strength of the radius diaphysis more accurately. Computed tomography 2

3 (CT)-based FEMs are known to provide accurate predictions of fracture loads for femurs (Cody DD et al., 1999; Keyak JH et al., 1998; Keyak JH et al., 2001; Dragomir-Daescu D et al., 2011), vertebra (Imai K et al., 2006; Silva MJ et al., 1998; Liebschner MA et al., 2003; Crawford RP et al., 2003), and the distal radius (Edwards WB and Troy KL, 2012). Keyak et al. reported that the patient-specific, nonlinear FE models provide an unprecedented level of precision for predicting proximal femoral fracture load (Keyak JH et al., 2001). To our knowledge, no previous studies document using patient-specific, CT-based, nonlinear FEMs to measure radial diaphysis fracture strength. Moreover, there are no previous studies evaluating the influence of the metal artifact by plate fixation to CT-based FEM strength prediction. Therefore, the aim of this study was to evaluate plated radial diaphysis strength using patient-specific, CT-based, nonlinear FEMs and to gauge the accuracy of this prediction against measurements of actual fracture strength in a cadaveric model Methods Specimens Fourteen intact radii were harvested from 8 fresh frozen cadavers obtained from our university s clinical anatomy laboratory. Specimens were obtained from 3 females and 5 males with a mean age of 83.9 years, range years. Radii were thawed at room temperature just before examination by CT and were not refrozen. Before CT scanning, all soft tissue was removed. Specimens were continuously moistened with a sprayed saline solution. An osteotomy was performed to remove the proximal and distal one-sixth of each radius (Fig. 1). Radii were divided into two groups, shown in Figure 1: 1) intact radii (a) and 2) radii with a locking plate affixed to simulate fracture reduction with hardware (b). The group of intact 3

4 radii was used to evaluate the accuracy of bone strength predictions of the FEM technique. Radii-affixed plates were used to evaluate the influence of the metal artifact in CT imaging on mineral density characterization and modeling of bone strength. 8-hole locking plates (Limited Contact-Locking Compression Plate, (LC-LCP), Synthes, West Chester, PA, USA) were fixed on the center of the radius parallel with the volar aspect of distal radius joint edge using six screws. The plate was initially fixed with 2 cortical screws in the 3 rd holes from the proximal and distal ends. Fixation was completed with four additional locking screws inserted proximal and distal to the initial two screws. Computed Tomography All radii were imaged using Computed Tomography (CT) (Aquilion ONE; Toshiba Medical Systems, Tokyo, Japan, 320-row detector 120 kv, 200 ma, slice thickness 0.5 mm, pixel width 0.3 mm, pitch 0.516). The intact radii group were scanned once, while the plated radii group were scanned with plates attached and once again with the plates and screws removed. These data allowed for creation of two groups to evaluate bone strength: an actual plate removal group and a simulated plate removal group. After scanning, the extant 2-cm of each end of the radii were potted in resin bone cement to aid in gripping during mechanical testing Nonlinear Finite Element Method CT data were imported using an FEA software package (Mechanical Finder, Research Center for Computational Mechanics, Tokyo, Japan) for constructing non-linear, subjectspecific, three-dimensional models. Radii were segmented by defining a region of interest (ROI) which included pixels with intensity greater than 1000 Housfield units (HU). For scan data of the simulated plate removal group, the ROI of the plate and screws was defined to include pixels with intensity greater than 3000 HU. Bone was meshed using linear 4

5 tetrahedral elements with a 1.2-mm global edge length, and the outer surface of the cortical bone was modeled using 1.2 mm triangular shell elements to compensate for strength losses resulting from CT resolution effects. The virtual thickness of the shell element was set as 0.4 mm. For the simulated plate removal group, radius models were made after simulated hardware removal, (i.e. the hardware ROI was subtracted from that of the bone using a Boolean operation, and remaining material was meshed). The resin cement caps on the radius ends were meshed with linear tetrahedral elements with a 1.2-mm global edge length. Bone heterogeneity was modeled by defining mechanical properties of each element based on corresponding Hounsfield unit (H.U.) value at their location, as indicated in Equation 1. The ash density of each element was set as the average ash density of the voxels contained in the space of that element Ash density [g/cm 3 ] = (H.U ) 0.001/1.0580: (H. U. value > 1) - Equation 1 Ash density [g/cm 3 ] = 0.0 : (H. U. value 1) Young s modulus and the yield stress for each tetrahedral element, assumed to be isotropic, were calculated from the equations proposed by Keyak et al. [11]. Any modulus calculated to be 20 GPa or greater were assigned a value of 20 GPa, a reasonable value define the extreme for cortical bone. To prevent the influence of a metal artifact, ash densities greater than 2.0 g/cm 3 were assigned a value of 2.0 g/cm 3, again, a reasonable value defining the extreme of cortical bone. The Young s modulus used for the shell was the value of the next tetrahedral element with a H.U. value of at least 600. Poisson s ratio for each element was set as 0.3, as used in previous reports (Muller M et al., 2008). Young s modulus and Poisson s ratio for each element of resin cement were set as 4.0 GPa 5

6 and 0.4, respectively. Adhesive contact between resin and bone was assigned. A uniform displacement with was applied to the resin cement at the distal end of the radius at ramped displacement increments of 0.01 mm up to the displacement until the failure criteria was reached (Fig. 2). Resin cement elements at the proximal end of the radius were encastred. Each element was assumed to yield when its Drucker Prager equivalent stress reached the element yield stress. From FEA results, the force/displacement curve was plotted and the fracture load was identified by a rapid decline in load (Fig. 3). Sites where elements yielded were analyzed Quasi-Static Uniaxial Compressive Load Testing In order to assess actual fracture loads, specimens were loaded in compression using an Autograph DCS-2000 universal testing machine (Shimadzu, Kyoto, Japan). Force was applied to the distal cement block and the proximal cement block was completely constrained. The actuator was driven under displacement control at a rate of 5 mm/min until fracture of the radial diaphysis occurred. The fracture load was identified by a rapid decrease in the slope of the force/displacement curve. Fracture loads predicted by FEM were compared to the measured fracture loads using a paired t test and Pearson s correlation coefficient. A P value <0.05 was considered statistically significant Influence of the Metal Artifact on BMD and Strength Bone mineral density in the actual plate removal group and the simulated plate removal group were assessed from CT DICOM data. The mineral density was measured over a 3-cm distance in two regions beneath the plate, one region was the half adjacent to the plate and the other was the half opposite the plate (Fig. 4). The BMD of two groups were compared and analyzed using a paired t test. 6

7 As was similarly done with intact radii data, we compared the FEM-predicted fracture loads in the actual plate removal group with the physical fracture loads measured from compression testing of the same radii with a plate affixed. To determine the influence of the metal artifact on strength predictions, we compared the FEM-predicted fracture loads between the simulated removal group and actual plate removal group. To determine that the simulated removal process could accurately predict the bone strength, we compared the FEM-predicted fracture loads of the simulated removal group with the measured fracture load. The data from each group were compared and analyzed using a repeated measures ANOVA and for multiple comparisons, we used a Bonferroni correction. The data from both methods were compared and analyzed using Pearson s correlation coefficient Results Accuracy of Bone Strength Using FEM No signs of comminuted fracture lines or compressive fracture lines were identified on any radial diaphysis. Fracture lines in mechanically-tested specimens coincided with the region of the failed elements in the every FEA models. The mean (SD) mechanically-tested and FEA-predicted fracture loads in the intact group were (217.7) N and (1252.9) N, respectively. There was no significant difference between them (p = 0.86). There was a significant linear correlation between the FE predicted fracture loads and the measured loads (r = , P < ) and the slope of the regression line was (Fig.5) The Influence of the Metal Artifact Mean(SD) mineral densities of the bone adjacent to the plate in the actual plate removal and 7

8 simulated plate removal groups were (0.2511) g/cm 3 and (0.2639) g/cm 3, respectively. Mineral densities of the bone opposite to the plate in the actual plate removal and simulated plate removal groups were (0.2627) g/cm 3 and (0.3540) g/cm 3, respectively. There were no significant difference between them (p = 0.38 and 0.27, respectively). However, in the simulated plate removal group, the mineral density tended to be higher, with a mean 4.98% higher in bone adjacent to the plate and 7.91% higher in bone opposite the plate, on average. Figure 3 showed a representative fracture for one specimen; we compared the fracture site (Fig.3a) from photo, a CT image and the FE-simulated result (Fig. 3b). Actual fracture load, and FE-predicted failure loads from the simulated and actual removal groups were N, N and N, respectively. The mean (SD) fracture loads of the plated and mechanically-tested, actual plate removal and simulated plate removal groups were (1676.4) N, (1493.1) N and (2347.3) N, respectively. There was no significant difference between the mechanically-tested data and the actual plate removal data (p = 0.46). However, the predicted bone strength in the simulated plate removal group was significantly higher than mechanical test measurements (p < 0.05), 32.3% higher on average. The actual plate removal group fracture loads were linear correlated with the mechanical test data (r = , p < 0.01) with a regression line slope of (Fig. 6a). The simulated plate removal data and the mechanical test were also highly correlated (r = , p < 0.01) with a regression line slope of (Fig. 6a). In addition, the predicted fracture loads in actual plate removal and simulated plate removal groups were excellently correlated (r = , p < 0.01). However, the fracture load in simulated removal group overestimated fracture load, moreso compared with that of the actual removal group, as indicated by the slope of the regression. (Fig. 6b) 200 8

9 Discussion In the present study, the correlation between experimental measurements of bone strength and predicted measurements using patient-specific, CT- based, nonlinear FEMs was very good and independent of whether plate fixation was performed or not. The characteristics of the FEM used in the present study are (1) use of tetrahedral elements to model an accurate surface form for the entire radial diaphysis, (2) use of nonlinear analysis to match the elastoplasticity of the radial diaphysis of fresh frozen cadaver specimens in compression, (3) construction of cortical shells on the surface of the model, and (4) use of Drucker Prager equivalent stress as an element yield criterion instead of von Mises yield criterion. There are a number of reasons why this selection of model parameters is ideal for this application. In practice, a bone surface contour is created more precisely and accurately with tetrahedral elements than with hexahedral elements. Therefore, it is possible to avoid artifacts in the external structure. We could automatically construct tetrahedral mesh elements more easily than creating any other meshed structure, while we could not construct quadratic tetrahedral or quadratic hexagonal elements. The method is quite simple, and even a novice can construct a meshed model using tetrahedral elements in a few minutes, even if the model has as many as one million elements. However, only highly experienced users can construct quadratic tetrahedral or quadratic hexagonal elements, which can require hours or even days. Naturally, we believe that quadratic elements or hexagoanl elements are much more accurate. However, in the clinic it is important to use software that can be used easily and quickly. Currently, CT resolution is so coarse that the density of the bone edge tends to be underestimated. Because the material properties the shell elements are dependent on their corresponding H.U. value, the strength of the shell elements tends to be weaker. In previous 9

10 studies on vertebral bone, the thickness of the shell element was set as mm and Young s modulus was set as GPa (Imai K et al., 2006; Liebschner MA et al., 2003; Overaker DW et al., 1999). However, there is no previous report regarding the optimal thickness of the cortical shell in the radius diaphysis. We set the thickness as 0.4 mm and Young s modulus for the shell as the value in the next tetrahedral element with a H.U. value of at least 600, after a preliminary analysis to determine these variables. Bosisio et al. demonstrated an apparent elastic modulus ranging between 10.4 and 18.7 GPa for the mid-shaft of the human radius (Bosisio MR et al., 2007). However, human bone density varies for each specimen, time, bone, and site. Keyak et al. proposed nonlinear equations to determine the value of Young s modulus and yield stress from the H.U. and reported that the correlation between measured values of bone strength with the FEM was excellent in the femoral neck (Keyak JH et al., 2001). The correlation between the measured values of bone strength using the FEM with the equations was remarkably good. The metal plate implant produces artifact and the H.U values surrounding the implant are altered from values that would be recorded if the plate was not present. A previous study demonstrated the influence of the metal artifact in CT imaging (van der Schaaf I et al., 2006; Boas FE and Fleischmann D, 2011). The degree of artifact is related to several factors, including the composition of the metal, the orientation and shape of the hardware, the thickness of the metal, and the intrinsic scanning parameters (White LM and Buckwalter KA, 2002; Sofka CM et al., 2006; Buckwalter KA et al., 2006; Berg BV et al., 2006). However, to our knowledge, the influence of the metal artifact on non-linear, specimenspecific, CT-based FEM has not been reported. In this study, we demonstrated the influence directly, and its applicability to clinical studies. When the mineral density is predicted for patients with a fixed titanium plate, multiplying these values by a region-based correction factor should adequately correct the effect of the artifact. For example, in this study we 10

11 found factors of or could be applied to correct mineral density values adjacent to and opposite to the plate, respectively. In present study, the correlation between actual measurements of bone strength and the predicted measurement using a patient-specific, CT- based, nonlinear FEM was very good regardless of whether plate fixation was performed or not. Moreover, this study demonstrated the extent of the influence of metal artifact. To our knowledge, no previous studies document using patient-specific, CT-based, nonlinear FEMs to measure radial diaphysis fracture strength clinically. Clinical use of this measurement method would allow prediction of patient forearm bone strength with or without plate fixation. This method may be a powerful tool for evaluating bone atrophy in the long term after plate fixation. This study has several limitations, the most important of which is that all of the cadavers were from elderly subjects with osteoporosis. The strength of a radial diaphysis without osteoporosis may not be able to be predicted by the FE model used in this study. Second, we did not use a calibration phantom, and the H.U. value might vary to some extent in the CT environment. Nevertheless, we demonstrated a strong relationship between the actual fracture forces and their prediction using FEM without a calibration phantom. Therefore, we believe that the error in H.U. without the use of a calibration phantom might be small, and that the equation is useful. In this study, the elements were assumed to be directionally isotropic. The Mechanical Finder software cannot create an anisotropic material model. The radius diaphysis might have anisotropic characteristics because of its trabecular pattern. We believe that this directional anisotropy might contribute to some errors. Finally, the predicted fracture load determined by FEM is approximate. We used the upper limit as a threshold. The true predicted fracture load at which the slope of forcedisplacement curve was decreased between the final 0.01 mm and less than the tested bone 11

12 failure displacement, because the bone failure was simulated by applying a ramped displacement in increments of 0.01 mm up to the displacement at which critical fracture occurred. However, the differences found are highly insignificant and, therefore, this limitation likely does not substantially affect the conclusion we reached. The present study shows that the strength of the radial diaphysis was accurately predicted using a specimen-specific, CT-based, nonlinear FE model. Additional studies should be performed to evaluate patient bone strength in a clinical application Acknowledgment We thank Chisato Mori, Kenji Tsubota, Ryo Hiwatari, Kenichi Murakami, Ken Hashimoto, Seiji Okamoto, Masataka Shibayama, Tomoko Kobayashi, Nahoko Iwakura, Noriyuki Yanagawa, Naoki Hara, Hideyuki Mimata, Shigeru Matsunaga, Ayako Takiguchi, and all of radiorogists for technical assistance References Berg BV, Malghem J, Maldague B, Lecouvet F. Multi-detector CT imaging in the postoperative orthopedic patient with metal hardware. Eur J Radiol. 2006; 60: Boas FE, Fleischmann D. Evaluation of two iterative techniques for reducing metal artifacts in computed tomography. Radiology. 2011;259: Bosisio MR, Talmant M, Skalli W, Laugier P, Mitton D. Apparent Young s modulus of human radius using inverse finite-element method. J Biomech. 2007;40: Buckwalter KA, Parr JA, Choplin RH, Capello WN. Multichannel CT imaging of orthopedic hardware and implants. Semin Musculoskelet Radiol. 2006;10:

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